PSLE Ken designed a logo as shown. The logo is made up of 2 small identical quarter circles, a large quarter circle and two straight lines drawn inside a square of side 63 cm. The radius of each small quarter circle is 21 cm.
- What is the perimeter of the shaded part?
- What is the area of the shaded part?
(a)
Radius of the large quarter circle
= 63 - 21
= 42 cm
Perimeter of the large quarter circle
=
14 x 2 x
227 x 42
= 66 cm
Perimeter of 2 small quarter circles
=
12 x 2 x
227 x 21
= 66 cm
Difference in the radii between the large quarter circle and the small quarter circle
= 42 - 21
= 21 cm
Perimeter of the shaded part
= 21 + 21 + 21 + 21 + 66 + 66
= 216 cm
(b)
Area of the two quarter circles
= 2 x
14 x
227 x 21 x 21
= 693 cm
2 Area of the boomerang
= 42 x 42 -
14 x
227 x 42 x 42
= 1764 - 1386
= 378 cm
2 Area of the shaded part
= 693 + 378
= 1071 cm
2 Answer(s): (a) 216 cm; (b) 1071 cm
2